I'd leave it full...emptying it would just introduce more oxygen and potentially rust. Now, depending on how long it was unused, I'd consider flushing it before reuse or, turn the temp up to max and let it sit for awhile before turning it back down. You might want to turn the supply water off, then, if it developed a leak, at least it would be limited to what was stored in the tank rather than an unlimited supply.

The pilot will burn on the order of ~5 therms/month, but the exhaust from that tiny flame condenses on the flue & heat exchanger. In normal operation that condensation isn't an issue since it gets re-heated and blown away multiple times/day on real burns, but for months on end it will (however slightly) corrode the fire-side of the heat exchanger, resulting in slightly lower combustion efficiency. It's pretty minor if it's only a week or two at a time.

Turning off the gas to unused appliances when going away for months at a time increases the odds that the house will still be there when you get back too, eh?